<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>des2ss</title>
  </head>
  <body bgcolor="#FFFFFF">
    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>des2ss</b> -  descriptor to state-space</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Sl]=des2ss(A,B,C,D,E [,tol])  </tt>
      </dd>
      <dd>
        <tt>[Sl]=des2ss(Des)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>A,B,C,D,E</b>
        </tt>: real matrices of appropriate dimensions</li>
      <li>
        <tt>
          <b>Des</b>
        </tt>: list</li>
      <li>
        <tt>
          <b>Sl</b>
        </tt>: <tt>
          <b>syslin</b>
        </tt> list</li>
      <li>
        <tt>
          <b>tol</b>
        </tt>: real parameter (threshold) (default value <tt>
          <b>100*%eps</b>
        </tt>).</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Descriptor to state-space transform.</p>
    <p>
      <tt>
        <b>Sl=des2ss(A,B,C,D,E)</b>
      </tt> returns 
    a linear system <tt>
        <b>Sl</b>
      </tt> equivalent to the descriptor system 
    <tt>
        <b>(E,A,B,C,D)</b>
      </tt>.</p>
    <p>
    For index one <tt>
        <b>(E,A)</b>
      </tt> pencil, explicit formula is used and
    for higher index pencils <tt>
        <b>rowshuff</b>
      </tt> is used.</p>
    <p>
      <tt>
        <b>Sl=des2ss(Des)</b>
      </tt> with <tt>
        <b>Des=list('des',A,B,C,D,E)</b>
      </tt> returns
    a linear system <tt>
        <b>Sl</b>
      </tt> in state-space form with possibly 
    a polynomial <tt>
        <b>D</b>
      </tt> matrix.</p>
    <p>
    A generalized Leverrier algorithm is used.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

s=poly(0,'s');G=[1/(s-1),s;1,2/s^3];
S1=tf2des(G);S2=tf2des(G,"withD");
W1=des2ss(S1);W2=des2ss(S2);
clean(ss2tf(W1))
clean(ss2tf(W2))
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../control/des2tf.htm">
        <tt>
          <b>des2tf</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/glever.htm">
        <tt>
          <b>glever</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/rowshuff.htm">
        <tt>
          <b>rowshuff</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
  </body>
</html>
